finish max sum sub arr

Author: CheYulin

bioinformatics/dynamic_programming/max_sum_sub_arr.py

@@ -0,0 +1,59 @@
+import numpy as np
+
+
+def inclusive_scan(num_list):
+    ret_list = []
+    sum_val = 0
+    for num in num_list:
+        sum_val += num
+        ret_list.append(sum_val)
+    return ret_list
+
+
+# inclusive i, j
+def min_max(i, j, num_list):
+    assert 0 <= i <= j <= len(num_list)
+    min_idx, max_idx = i, i
+    min_val, max_val = num_list[i], num_list[i]
+    for idx in xrange(i + 1, j + 1):
+        if min_val > num_list[idx]:
+            min_idx, min_val = idx, num_list[idx]
+        if max_val < num_list[idx]:
+            max_idx, max_val = idx, num_list[idx]
+    return min_idx, max_idx
+
+
+def max_difference(i, j, num_list):
+    # condition
+    if i > j:
+        return -1, -1, -np.inf
+    else:
+        min_idx, max_idx = min_max(i, j, num_list)
+        if min_idx <= max_idx:
+            return min_idx, max_idx, num_list[max_idx] - num_list[min_idx]
+        else:
+            cur_min_idx, cur_max_idx = min_max(i, max_idx, num_list)
+            cur_max_differ = num_list[cur_max_idx] - num_list[cur_min_idx]
+
+            new_min_idx, new_max_idx = min_max(min_idx, j, num_list)
+            new_max_differ = num_list[new_max_idx] - num_list[new_max_idx]
+
+            if new_max_differ > cur_max_differ:
+                cur_min_idx, cur_max_idx = new_min_idx, new_max_idx
+
+            middle_min_idx, middle_max_idx, middle_max_differ = max_difference(max_idx + 1, min_idx - 1, num_list)
+            if middle_max_differ > cur_max_differ:
+                cur_min_idx, cur_max_idx, cur_max_differ = middle_min_idx, middle_max_idx, middle_max_differ
+
+            return cur_min_idx, cur_max_idx, cur_max_differ
+
+
+if __name__ == '__main__':
+    input_list = [1, -2, 3, 10, -4, 7, 2, -5]
+    scan_list = inclusive_scan(input_list)
+    print input_list
+    print scan_list
+    print max_difference(0, len(scan_list) - 1, scan_list)
+
+    scan_list1 = [2, 4, 7, -1, 3, 6, -2, 4]
+    print max_difference(0, len(scan_list1)-1, scan_list1)